Search

Starting from a noncommutative algebra {ital scrA} of the form {ital scrC}{direct product}{ital scrM}, where {ital scrC} is the algebra of smooth functions on space-time and {ital scrM} is the algebra of {ital n}{times}{ital n} Hermitian matrices, we construct an exterior algebra of differential forms over {ital scrA}. We use the one-forms of this algebra to describe Yang-Mills and Higgs fields on a similar footing and construct a Lagrangian from its two-forms. We show how, in the resulting geometrical description, a Higgs potential that leads to spontaneous symmetry breaking arises naturally. We discuss the application of this formalism to the bosonic sectors of the standard electroweak theory and a grand-unified model based on SU(5){direct product}U(1).

The formalisms of spontaneous symmetry breaking and of the theory of nonlinear Lagrangians are reviewed, with emphasis on the relationships between the two. The former is applied to the Weinberg-Salam model, in which case the physical fields and their explicit transformation laws under finite group action are exhibited. The latter is illustrated through the example of the graded Lie group OSp(1/4). Locally covariant fields and derivatives are then constructed, and invariant terms are written down which contain the Lagrangian of supergravity.

Four-dimensional second-order supersymmetric equations involving an arbitrary function of an unconstrained chiral superfield are proposed. In three dimensions a new invariant operator provides the generalization of analogous two-dimensional equations that are of first order in the fermion field.

The relevance of the representation theory of the conformal group to quantum field theory is illustrated in two dimensions by the Thirring model. Space-time position operators and their complex extensions are defined as operator-valued functions of the generators. These complex position variables coincide with the Gel'fand-Naimark labels and can be interpreted as labels for nonorthogonal coherent states. A Hilbert-space metric then becomes necessary. It is given by the matrix elements of the metric operator $G$ and is nontrivial for the nonanalytic supplementary series and the analytic representations. In this case ${G}^{\ensuremath{-}1}$ gives the two-point function for the Thirring model. For nonanalytic representations only weak (infinitesimal) conformal invariance holds for interacting fields if causal and spectral properties are imposed, while those properties become compatible with strong (global) conformal invariance in the case of analytic representations which lead either to free fields or to interacting fields with a quantized value of the coupling constant.

We propose an alternative arising naturally in a six-quark model to the Glashow--Iliopoulos--Maiani mechanism for the suppression of $delta$S = 1 neutral currents. While violating the Cabibbo form of universality, it maintains the tan$sup 2$ theta/sub C/ suppression of strange particle decays and introduces an additional tan theta/sub C/ suppression of charmed-particle decays. (AIP)

x 5(x' —z'{s))5(x' —z'(s }) is the mass density which is infinite on the world line z =z (s) of the singularity and zero elsewhere. Because of the scalar density character of the 6 function the left-hand side of Eq. (2} is a tensor density. From Eq. (1) follows the conservation law The string equation of motion was further studied by many authors' ' in connection with duality. The purpose of this note is to show that the worldsheet equation (8) can be derived in general relativity following Einstein's method for the geodesic world line.